We are long time kayakers having shifted with age from whitewater to flat-water on the lake. There being no simple quick answer, I offer the following:
1. Always have every paddler wear a PFD. Simply having it in the boat does not do it. If one dumps and there is some wind, your boat may float away faster than you can swim to it.
2. If you aim is just having short distance wet fun with inexperienced paddlers, get one of the short (15' or less) wide tubs. Inexpensive and good initial stability but very slow and no secondary stability. We see a lot of these going around the island; it is rare to see one occupied by a paddler with good paddling skills however.
3. If your aim is going some distance and being able to deal with whatever conditions that may arise, then you need a longer (16' to 17') narrower boat along with some basic skills. Actually such a boat while narrower and with a rounded bottom, is more stable in rough water provided you have some skill. In this case, 1st take a lesson in a rental boat and get some advice. There are some places around, Google found:
http://www.wildmeadowcanoes.com/wmtest.swf
Have fun and be safe.